Mister Exam

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Identical expressions
3dx/cos^ two x/2
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3dx/cos²x/2
3dx/cos to the power of 2x/2
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Integral of 3dx/cos^2x/2 dx

The solution

You have entered [src]

 pi             
 --             
 2              
  /             
 |              
 |  /   3   \   
 |  |-------|   
 |  |   2   |   
 |  \cos (x)/   
 |  --------- dx
 |      2       
 |              
/               
pi              
--              
3

$$\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{3 \frac{1}{\cos^{2}{\left(x \right)}}}{2}\, dx$$

Integral((3/cos(x)^2)/2, (x, pi/3, pi/2))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{3 \frac{1}{\cos^{2}{\left(x \right)}}}{2}\, dx = \frac{\int \frac{3}{\cos^{2}{\left(x \right)}}\, dx}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3}{\cos^{2}{\left(x \right)}}\, dx = 3 \int \frac{1}{\cos^{2}{\left(x \right)}}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
  So, the result is: $\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}}$
So, the result is: $\frac{3 \sin{\left(x \right)}}{2 \cos{\left(x \right)}}$
Now simplify:

$\frac{3 \tan{\left(x \right)}}{2}$
Add the constant of integration:

$\frac{3 \tan{\left(x \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 \tan{\left(x \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                            
 | /   3   \                  
 | |-------|                  
 | |   2   |                  
 | \cos (x)/          3*sin(x)
 | --------- dx = C + --------
 |     2              2*cos(x)
 |                            
/

$$\int \frac{3 \frac{1}{\cos^{2}{\left(x \right)}}}{2}\, dx = C + \frac{3 \sin{\left(x \right)}}{2 \cos{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

Numerical answer [src]

2.44822697959396e+16

2.44822697959396e+16

Use the examples entering the upper and lower limits of integration.

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Identical expressions

Integral of 3dx/cos^2x/2 dx

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The solution